While it is a paradox to go back in time and kill your grandfather, physicists agree there is no paradox if you go back in time and save him from being hit by a bus.Is this really true? I can't see how.
Suppose your (saved) grandfather goes on to sire a child who grows up to be Hitler (or, to the good, FDR). By intervening you have clearly changed history -- Hitler/FDR would not be born if you hadn't intervened, but will be born if you had. How can there be no paradox, in either case?